A Wide Tuning-Range mm-Wave LC-VCO Sized Using Evolutionary Algorithms A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Honors Research Distinction in the The Ohio State University By Matthew R. Belz, Undergraduate Program in Electrical and Computer Engineering The Ohio State University 2019 Research Distinction Committee: Dr. Waleed Khalil, Advisor Dr. Steven Bibyk Dr. Tawfiq Musah
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A Wide Tuning-Range mm-Wave LC-VCO Sized Using
Evolutionary Algorithms
A Thesis
Presented in Partial Fulfillment of the Requirements for the DegreeHonors Research Distinction in the The Ohio State University
By
Matthew R. Belz,
Undergraduate Program in Electrical and Computer Engineering
This work has presented a methodology for rapidly designing a VCO suitable for
use at mm-Wave frequencies. The segmented C-DAC topology described in Chapter
3 allows for a wide TR while maintaining low PN. Cost surfaces based on simulation
data allow for rapid fitness evaluation while still maintaining a high level of accuracy.
Additionally, this allows for rapid re-designs in new technology nodes by updating
the cost surface data from the circuit simulator.
3.2 Broader Impacts
The design of a VCO is a time consuming process and also requires expert knowl-
edge to complete a working design. In industry, time-to-market is often a critical
factor and using an evolutionary algorithm such as presented in this work can reduce
the design time by determining a good starting point for further manual tuning if
required. This can especially be helpful when a new technology node is used since
the designer will need to learn new guidelines on how the device sizes correlate to
performance.
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Defense contractors and government labs also may find this work useful since
their focus is based on missions which are constantly changing. The ability to design
a custom ASIC without expert designers in every RF sub-block is a topic of current
research through the DARPA electronics resurgence initiative (ERI). In defense ap-
plications, some performance degradation from the state-of-the-art may be tolerable
as long as the mission requirements are met.
Both industry and government labs could benefit from the ability to use artificial
intelligence for circuit design by reducing the required engineering hours and free up
designers to consider more creative architectures instead of manually perturbing the
component sizes to determine the optimal conditions.
3.3 Future Work
As technology nodes continue to scale, simulations based on schematic designs are
becoming increasingly poor at predicting performance as layout parasitics become
more dominant. Currently the GA uses parametric sweep data from a schematic-level
simulation and assumes proper layout will give the designer similar (but degraded)
performance. If the layout is generated along with the schematic representation, the
parasitics due to the layout can also be considered leading to a more accurate in-
dication of performance once the device is fabricated. Additionally, for mm-Wave
frequencies the inductor and feed line network should be measured using an electro-
magnetic (EM) simulator and included during the optimization. For this work it was
assumed that the PDK inductor simulation was sufficiently accurate and the feed line
parasitics were negligible. The Berkeley Analog Generator would be a good platform
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to build a layout aware GA since it has interfaces to both circuit and EM simulators
using layout extracted parasitics in simulation runs [17].
While the GA optimizes for the component sizing, there are still several aspects
which must be designed manually such as the biasing circuitry. The bias circuits not
only have a significant impact on the noise of the device [18], but they also impact
the figure of merit through the power consumption. If the bias current is added as a
parameter in the algorithm, the power consumption could also be optimized automat-
ically instead of tuning based on designer intuition. By optimizing the bias current
the PN can also be minimized by operating at the boundary between the current
limited and voltage limited operating regions for the VCO. Additionally second order
effects such as supply pushing are not considered, but are a critical specification for
many applications.
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Appendix A: Collaboration
This appendix discusses the collaboration during the completion of this work. The
circuit field is moving away from absolute maximum circuit performance to generator
based design where a circuit generator can design several different custom circuits
based on an initial topology to serve different application requirements. My work
has been some of the first at the CLASS group to address this growing need in the
circuit community for rapid design and optimization. Dr. Shahriar Rashid helped
me to understand the details of traditional circuit design, and in turn, I was able
to further his understanding of how the design space can be mapped into an opti-
mization framework. A similar collaboration occurred with Saeed Alzahrani who also
specializes in VCO design. Over the summer I also did some preliminary work for
VCO optimization with layout parasitics using the Berkeley Analog Generator. This
required installing and customizing environments on our servers to run. Dr. Luke
Duncan later used the BAG environment that I helped setup for his own projects.
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Appendix B: MATLAB Code
This appendix lists the most important MATLAB scripts and functions required
for the genetic algorithm. The main function is VCO main GA3.m and this is where the
GA run is initiated. This function will call all other necessary functions for the opti-
mization. VCO fitness5.m is the function that determines the fitness of any given so-
lution. The scripts import digitalCapSweep min5mA2.m and S parameter Cleanup.m
are import scripts which do some processing so they are also included for complete-
ness.
code/VCO main GA3.m
1 % Main GA S c r i p t f o r VCO with d i g i t a l tuning caps2 % Matthew Belz 2/22/201934 %[ f itresult CAPH , gof1 ] = fitDigCapWL (w, capL , CapEQ high ) %
Overa l l cap HIGH t r a n s i s t o r dependance5 close a l l67 %f i t f u n c t i o n s f o r the switched cap un i t8 [ f itCapHigh , go f1 ] = fitDigCapWL2 (NF, capL , CapEQ high )9 [ fitCapLow , gof2 ] = fitDigCapWL2 (NF, capL , CapEQ low)
10 [ fitRpON , gof3 ] = fitDigCapWL2 (NF, capL , RP ON EQ)11 [ fitRpOFF , gof4 ] = fitDigCapWL2 (NF, capL , RP OFF EQ)12 [ f itm , go f5 ] = fitDigCapWL2 (NF, capL , mEQ)1314 % Fit f u n c t i o n s f o r c ros s−coupled pa i r15 [ fitGMxWid y , go f ] = fitGMxWxcplY(Gm, Wxcpl ) ;16 [ f itCxcplusingGm , go f ] = gmXCxcplY(Gm, Cxcpl ) ;17
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1819 % [NF, CapL , varW , varNF ]202122 lb1 =[1 ,3 .2 e−6, 2 .56 e−7, 1 ] ; %l a s t element i s f i x e d cap23 ub1 =[20 ,60 e−6, 10e−6, 2 0 ] ;2425 % L f o r now s e t26 % l a r g e s t width and s m a l l e s t outer dimension s imulated
inductance at 28G27 L=130.7e−12;28 L rp= RpIND avg ; % average Rp f o r OD=100u , Wid=12.25u f r e q
sweep 22−32GHz2930 opts1= opt imopt ions (@ga , . . .31 ’ Popu lat ionS ize ’ , 200 , . . .32 ’ MaxGenerations ’ , 60 , . . .33 ’ El i teCount ’ , 2 , . . .34 ’ Const ra intTo le rance ’ , 5 , . . .35 ’ Funct ionTolerance ’ , 5 , . . .36 ’ PlotFcn ’ , @gap lotbes t f ) ;37 % rng (0 , ’ tw i s t e r ’ ) ;38 [ xbest , fbe s t , e x i t f l a g ] = ga (@( x ) VCO fitness5 (x , f itCapHigh ,
fitCapLow , fitRpON , fitRpOFF , fitm , fitCV0 , fitCV05 , fitRP02 ,f i tCV50percent , fitGMxWid y , fitCxcplusingGm , L , L rp ) , 4 ,[ ] , [ ] , [ ] , [ ] , . . .
39 lb1 , ub1 , [ ] , [ 1 , 4 ] , opts1 ) ;
code/VCO fitness5.m
1 function re tVal = VCO fitness5 (x , f itCapHigh , fitCapLow , fitRpON, fitRpOFF , fitm , fitCV0 , fitCV05 , fitRP02 , f i tCV50percent ,fitGMxWid y , fitCxcplusingGm , L , L rp )
2 % VCO Fi tne s s with switched caps3 % Matthew Belz 2/23/201945 % X = [ tranNF , CapL , varW , varNF ]67 %8 disp ( x (1 )+ ” ” + x (2) )9 C u n i t r a t i o = f i tm ( x (1 ) , x (2 ) )
10 %uni t cap C − b i t b011 C uni t h igh = fitCapHigh ( x (1 ) , x (2 ) )12 C unit low = fitCapLow ( x (1 ) , x (2 ) )
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13 % b i t b1 , 2C14 C unit h igh2=fitCapHigh ( x (1 ) , x (2 ) ) ∗2 ;15 C unit low2=fitCapLow ( x (1 ) , x (2 ) ) ∗2 ;16 % Thermo b i t s , 4C17 C unit h igh4=fitCapHigh ( x (1 ) , x (2 ) ) ∗4 ;18 C unit low4=fitCapLow ( x (1 ) , x (2 ) ) ∗4 ;192021 % Rp122 Rp2=fitRpOFF ( x (1 ) , x (2 ) )2324 Rp unit=fitRpON ( x (1 ) , x (2 ) ) ; % For C25 Rp 4unit=fitRpON ( x (1 ) , x (2 ) ) /4 ; % f o r 4C26 Rp 2unit=fitRpON ( x (1 ) , x (2 ) ) /2 ; %f o r 2C272829 % VARACTOR30 %Measured s i n g l e−ended with s i n g l e varac to r so I d i v id e by 231 C var high = fitCV05 ( x (3 ) , x (4 ) ) /2 ;32 C var low = fitCV0 ( x (3 ) , x (4 ) ) /2 ;33 C var 50percent=f i tCV50percent ( x (3 ) , x (4 ) ) /2 ;34 Rp var=fitRP02 ( x (3 ) , x (4 ) ) ∗2 % mult ip ly by 2 to account f o r
s i n g l e ended3536 % CROSS COUPLED PAIR3738 %Generate worst case Rp −− Al l ON, 2 binary b i t s , 7
thermometer caps39 Rp allON=1/(1/ Rp unit+1/Rp 2unit+1/Rp 4unit+1/Rp 4unit+1/
Rp 4unit+1/Rp 4unit+1/Rp 4unit+1/Rp 4unit+1/Rp 4unit +1/Rp var+1/L rp )
40 gm needed=2/Rp allON4142 % could use i f statement to make sure gm i s with in bounds43 i f ( gm needed < 0 .0159) && ( gm needed > 0 .004924)4445 Wxcpl=fitGMxWid y ( gm needed )46 Cxcpl=fitCxcplusingGm ( gm needed )47 else48 Wxcpl=0; %not sure what to put here49 Cxcpl=900e−15; % l a r g e cap50 end51
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5253 %Stray Cf ix capac i tance54 Cf ix=Cxcpl+10e−15; %gm pa i r and guess f o r b u f f e r5556 C mid=2∗C unit h igh4+C unit low4∗5+C uni t h igh+C unit h igh2+
C var 50percent+Cfix ; % middle f requency w i l l be at h a l fcap , mid curve
57 C mid minus1=1∗C unit h igh4+6∗C unit low4+C unit h igh2+C uni t h igh+C var 50percent+Cfix ; % f o r t e s t i n g over lap ,at middle o f curve above middle
58 C mid max= 2∗C unit h igh4+C unit low4∗5+C unit low+C unit low2+C var low+Cfix ; % Max frequency at mid coursetuning curve
5960 C min = 7∗C unit low4+C unit low2+C unit low+C var low+Cfix ;
% Max curve , and max on the curve ( varac to r low )61 C min minus1 mid = 7∗C unit low4+C unit low2+C uni t h igh+
C var 50percent+Cfix ; % Middle o f the curve on max −1curve
62 C min minus1 low= 7∗C unit low4+C unit low2+C uni t h igh+C var low+Cfix ;
63 C min high = 7∗C unit low4+C unit low2+C unit low+C var high+Cfix ; % Max curve , l owest f requency (max cap on that curve)
64 C min mid = 7∗C unit low4+C unit low2+C unit low+C var 50percent+Cfix ; % Max curve , middle f requency
656667 % Pr in t ing the C un i t s f o r c a l c u l a t i o n68 disp (” C unit low4 ” + C unit low4 )69 disp (” C unit low2 ” + C unit low2 )70 disp (” C unit low ” + C unit low )71 disp (” C var low ” + C var low )72 disp (” C min ” + C min )73 % both binary are o f f , add f i x e d cap74 % 01111 in binary i s 2ˆ4 or 15 , h a l f o f 2ˆ5 or 3175 % T7 T6 T5 T4 T3 T2 T1 T0 | B1 B076 % 0 0 0 0 0 1 1 | 1 17778 %C mid minus1 i s 14 or 0011 | 1079 %80 %0 0 0 0 1 1 1 | 1 081 % Low cap i s 0 0 0 0 0 0 0 | 0 0
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82 % C min=C unit low+C unit low2+7∗C unit low4+Cfix+C var low ;8384 C max=C uni t h igh+C unit h igh2+7∗C unit h igh4+C var high+Cfix
% a l l caps ON85 C max mid=C uni t h igh+C unit h igh2+7∗C unit h igh4+
C var 50percent+Cfix ;868788 f min =1/(2∗pi∗sqrt (L∗C max) ) % abso lu te min f , a l l caps OFF,
varac to r high89 f min mid =1/(2∗pi∗sqrt (L∗C max mid ) ) %Middle o f the lowest
curve9091 f mid =1/(2∗pi∗sqrt (L∗C mid ) ) % middle o f middle curve92 f max high =1/(2∗pi∗sqrt (L∗C min ) ) % abso lu t e max f = a l l caps
o f f ( and varac to r low )93 f max low =1/(2∗pi∗sqrt (L∗C min high ) ) % Highest curve , l owest
f r e q94 f max minus1 = 1/(2∗pi∗sqrt (L∗C min minus1 low ) )% h ighe s t
po int on second h ighe s t curve95 f max mid = 1/(2∗pi∗sqrt (L∗C min mid ) ) % Highest curve ,
middle f requency96 over lap= ( f max minus1−f max low ) /( ( f max high−f max low ) )979899 TR=f max mid−f min mid
100101102103104 % Find the over lap between curves105 % us ing the mid curve106107108 % Weights f o r ” normal ized ” f i t n e s s func t i on109 alpha=1e3 ;110 beta=1e−5;111 gamma=1E−5;112113 retVal = alpha∗abs(3−C u n i t r a t i o ) + beta∗1/Rp2 + 1E4∗1/
Rp var + gamma∗abs (28 e9−f mid ) + 1e6∗abs(0.4− over lap ) + 1E−6∗1/TR
114 %alpha∗abs(3−C u n i t r a t i o )+beta ∗1/Rp1
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115116117 end
code/import digitalCapSweep min5mA2.m
1 % imports d i g i t a l switched cap sweep v a r i b l e s and p r o c e s s e sthe data
10 RpON = importMOM2( ’ Rp ON swCap 60u . csv ’ , 2 , 102) ;11 Rp2 OFF = importMOM2( ’ Rp OFF swCap 60u . csv ’ , 2 , 102) ;121314 capL=caphigh ( : , 1 ) ;15 NF= [ 1 : 2 0 ] ;161718 % For m (Con/ Cof f ) r a t i o19 count2 =1;20 for k = 2 : 2 : 4 0 %Import as j u s t cap va lue s without capL
columns21 mEQ( : , count2 )=m( : , k ) ;22 count2=count2 +1;2324 end2526 % For high value o f cap27 count2 =1;28 for k = 2 : 2 : 4 0 %Import as j u s t cap va lue s without capL
columns29 CapEQ high ( : , count2 )=caphigh ( : , k ) ;30 count2=count2 +1;3132 end3334 % For low value o f cap35 count2 =1;
31
36 for k = 2 : 2 : 4 0 %Import as j u s t cap va lue s without capLcolumns
37 CapEQ low ( : , count2 )=caplow ( : , k ) ;38 count2=count2 +1;3940 end4142 % For Rp1 (ON)43 count2 =1;44 for k = 2 : 2 : 4 0 %Import as j u s t cap va lue s without capL
columns45 RP ON EQ( : , count2 )=RpON( : , k ) ;46 count2=count2 +1;4748 end4950 %For RP2 (OFF)51 count2 =1;52 for k = 2 : 2 : 4 0 %Import as j u s t cap va lue s without capL
columns53 RP OFF EQ ( : , count2 )=Rp2 OFF ( : , k ) ;54 count2=count2 +1;5556 end5758596061 %Generate cap Width sweep62 count =1;63 for i =1.22e−6:0.68 e−6:6.66 e−664 w( count )=i ;65 count=count +1;66 end6768 % Import the curves f o r the gm69 GmVsWxcpl = importGmPlot ( ’ gm wxcpl 5mA . csv ’ , 2 , 38) ;70 CxcplVsGm = importGmPlot ( ’ gm cin 5mA . csv ’ , 2 , 38 ) ;7172 %Generate ve c t o r s used in Curve f i t73 Wxcpl=GmVsWxcpl ( : , 1 ) ;74 Gm=GmVsWxcpl ( : , 2 ) ;75
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76 GmC=CxcplVsGm ( : , 1 ) ;77 Cxcpl=CxcplVsGm ( : , 2 ) ;78798081 % GmVsWxcpl = importGmPlot ( ’GmVsWxcpl2 . csv ’ , 2 , 38) ;82 % CxcplVsGm = importGmPlot ( ’ CxcplVsGm2 . csv ’ , 2 , 3 8 ) ;8384 %Generate ve c t o r s used in Curve f i t85 Wxcpl2=GmVsWxcpl ( : , 1 ) ;86 Gm2=GmVsWxcpl ( : , 2 ) ;8788 GmC2=CxcplVsGm ( : , 1 ) ;89 Cxcpl2=CxcplVsGm ( : , 2 ) ;
. . .8 1 i ∗sp28GHzW256nto25uNF1to25Lmin ( : , 3 : 2 : end) ;9 vo l tage = sp28 new ( : , 1 ) ;
10 s11 = sp28 new ( : , 2 : end) ;11 sp28 new y par t i a l = s11 ( : , 1 : 2 4 9 ) ;12 width =[256e−9 ,300e−9:100e−9:25e−6] ;13 y11 = (1/50)∗(1− s11 ) ./(1+ s11 ) ;14 f c = 28 e9 ;15 cap = imag( y11 ) . / ( 2∗ pi∗ f c ) ;16 c a p p a r t i a l = cap ( : , 1 : 2 5 ) ;17 NF = 1 : 1 : 2 5 ;18 c a p s u p e r p a r t i a l = c a p p a r t i a l ( 1 : 3 1 ) ;19 matr ix cap super = [ vo l tage ’ ; c a p s u p e r p a r t i a l ] ;20 c a p s u p e r p a r t i a l 2 = 1e16∗ c a p s u p e r p a r t i a l ;21 matr ix cap super2 = [ vo l tage ’ ; c a p s u p e r p a r t i a l 2 ] ;22 NF2=1 :1 : 25 ;232425 cap re form = reshape ( cap , 31 , 25 , 249 ) ;
33
26 V0=cap re form ( 7 , : , : ) ; % Not at zero V, at −0.2V f o r mostl i n e a r
27 V0sq=squeeze (V0) ;28 Vw=cap re form ( 7 , 1 , : ) ;2930 V05=cap re form ( 1 3 , : , : ) ; %s e l e c t s V=0.1V31 V05sq=squeeze (V05) ;3233 V50percent=cap re form ( 1 0 , : , : ) ; %s e l e c t s V=−0.05v f o r 50%
over lap measurement34 V50percentSq=squeeze ( V50percent ) ;3536 Rp=1./( real ( y11 ) ) ;37 Rp reform=reshape (Rp,31 , 25 , 249 ) ;38 Rp02=Rp reform ( 1 5 , : , : ) ; %Get Rp at 0 .2V39 Rp02sq=squeeze (Rp02) ;4041 surf ( width ’ , vo l tage ’ , squeeze ( cap re form ( : , 1 , : ) ) , ’ FaceColor ’ ,
’ r ’ )4243 %CO( : , : , 1 ) = ze ro s (31 ,99) ; % red44 %CO( : , : , 2 ) = ones (31 ,99) .∗ repmat ( l i n s p a c e ( 0 . 5 , 0 . 6 , 9 9 ) , 31 ,1 ) ;
% green45 %CO( : , : , 3 ) = ones (31 ,99) .∗ repmat ( l i n s p a c e (0 , 1 , 99 ) , 31 ,1 ) ; %
, 1 : 9 9 ) ) ∗1e15 , ’ FaceColor ’ , CO(NF, : ) , . . .55 ’ EdgeColor ’ , ’ k ’ , ’ L ineSty l e ’ , ’ : ’ )56 hold on57 end58 xlabel ( ’ Width (\mu m) ’ ) ;59 ylabel ( ’ Voltage (V) ’ ) ;60 zlabel ( ’ Capacitance ( fF ) ’ ) ;6162
34
63 %Generate s u r f a c e f o r V=0V64 [ fitCV0 , go f ] = createFitV0 ( width , NF2, V0sq ) ;65 %Generate func t i on f o r vo l tage at V=−0.266 [ fitCV05 , go f ] = createFitCV05 ( width , NF2, V05sq ) ;67 %Generate func t i on f o r vo l tage at V=0.1;68 [ f i tCV50percent , go f ] = createFitCV05 ( width , NF2,
V50percentSq ) ;69 %Generate func t i on f o r vo l tage at V=−0.05;70 [ fitRP02 , go f ] = createFitRP02 ( width , NF2, Rp02sq )71 %Generate func t i on f o r vo l tage at V=0.5p ;
35
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